On the principles of a spline extrapolation concerning geophysical data

TitleOn the principles of a spline extrapolation concerning geophysical data
Publication TypeJournal Article
Year of Publication2014
AuthorsKostinsky, AS
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published2/2014

Possible applications of spline mathematics applied to geophysical observations, when to build a physical dynamic model is either impossible or too complicated and unpractical, are discussed. In situations like this, the simple idea of spline extrapolation is determined uniquely: the net of knots on a specified segment is supplemented by a potentially predictable point, a "prognostic" spline on the augmented net is built, and it is necessary to ensure a minimum of the integral of the quadratic deviation depending on the add-on point ordinate as a parameter. For a uniform net base, structural units of the extrapolation algorithm are represented in the form of a sequence of expansions in terms of coordinates of the specified points, and the expansion coefficients are available analytically. It is found that the forecasted point ordinate does not depend on the net spacing, which is essential for the evaluation of the nearest next event in a series of regular measurements, when the basic thing is not the interval between measurements, but its constancy.

Keywordsgeophysical data, model, spline extrapolation

1. Zavialov Yu. S., Kvasov B. I., Miroshnichenko V. L. Methods of spline functions. Moscow: Nauka, 1980 (in Russian).
2. Vershynin V. V., Zavialov Yu. S., Pavlov N. N. Extreme properties of splines and the smoothing problem. Novosibirsk: Nauka, 1988 (in Russian).
3. Mogi K. Prediction of earthquakes. Moscow: Mir, 1988 (in Russian).
4. Romanovsky Yu. M., Stepanova N. V., Chernavsky D. S. Mathematical Biophysics. Moscow: Nauka, 1984 (in Russian).